As you develop a strong list of Twitter followers it becomes necessary to consistently put information in front of those people to keep them engaged. People do not read every single tweet in their news feed so you have to push out content to your followers at different times of day on an ongoing consistent basis.
The Tweet Old Post plugin allows for that. In addition to automatically tweeting on your behalf at a regularly defined interval, it will also introduce your followers to older content you have written which is good for your traffic and your SEO efforts.
Here is a video tutorial that will overview Tweet Old Post Plugin for WordPress